It is generally accepted that many pulsating X-ray sources are rotating magnetic neutron stars undergoing accretion. The text of this thesis provides a historical introduction to four studies, contained herein as appendices, in which we develop a theory of accretion by such stars. In these studies, we first give a detailed magnetohydrodynamic description of the accretion flow and the magnetic field configuration within the magnetosphere of the neutron star. We show that the accreting matter moves along the stellar field lines when viewed in the framecorotating with the star, and that the stellar field is azimuthally distorted by the matter. In the case of slow rotators, matter rotates in a sense opposite that of the net angular momentum flux toward the star. We then show that bounds on the accretion torque exerted on the star can be obtained by applying general conservation laws to the flow in the transition zone between the magnetospheric flow and the exterior flow,.even in the absence of detailed knowledge of the flow in this zone. Next, we determine the location, the size, and the structure of the transition zone
in the case of accretion from a Kepleri~n disk. The stellar magnetic field penetrates the inner part of the disk via the Kelvin-Helmholtz instability,
turbulent diffusion, and reconnection, producing a broad transition zone composed of two regions, a broad outer zone where viscous stresses dominate magnetic stresses, and a narrow inner zone or boundary layer where magnetic stresses dominate. We then calculate the accretion torque on the star. We
show that the magnetic coupling between the star and the plasma outside the inner edge of the disk makes an appreciable contribution to the accretion torque, and that the spin-up torque on fast rotators is substantially less than that on slow rotators as a result. For sufficiently high stellar angular velocities or sufficiently low accretion rates, the above coupling dominates that due to the plasma and the magnetic field at the inner edge of the disk, braking the star's rotation even while accretion, and hence X-ray emission,
continue.
Finally, we apply our results to pulsating X-ray sources, and show that the secular spin-up rates of all the measured sources, including Her X-I, can be accounted for quantitatively if one assumes that these sources are
10^29 - 10^32
i d have magnetic moments gauss
accreting from Kep1er an d1S" ks an . ~ 3
em. The present theory gives a "universal" relation between the secular spin-up rates, the periods, and the luminosities of the sources which adequately represents almost all the observational data, and provides statistical evidence for disk accretion in the observed sources. We show that the short-term period fluctuations and spin-down episodes observed in Her X-I, Cen X-3, Vela X-I and X Per follow from our model as consequences of fluctuations in
the mass accretion rate, and that for a fast rotator like Her X-I, fluctuations in the mass accretion rate can produce fluctuations in the accretion torque ~ 10^2 times larger. Further, spin-down episodes can be caused by reductions in the mass accretion rate, without ejection of mass from the vicinity of the neutron star. The spin-down torque at low accretion rates given by the present theory may account for the existence of a paradoxically large number of long period pulsating sources spinning up on short time scales, if these sources have "low" states during which the accretion rate is much reduced.